Constrained control for perturbed linear systems

The solution of the linear state feedback synthesis problem for a system affected by unknown but bounded noise with state and control bounds requires the evaluation of a positively D-invariant (PDI) and admissible set. Equivalent conditions such that a perturbed system admits compact and convex PDI sets of the polyhedral type are given, and equivalent conditions for the positive D-invariance of a polyhedron are presented. Algorithms for the evaluation of the maximal size of the disturbance set D compatible with the boundaries and for the approximation of the maximal PDI set contained in the state constraint set are proposed. Both continuous and discrete-time systems are considered